{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "f0208ef1",
   "metadata": {},
   "source": [
    "# rf604_constraints\n",
    "Likelihood and minimization: fitting with constraints\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "**Author:** Wouter Verkerke  \n",
    "<i><small>This notebook tutorial was automatically generated with <a href= \"https://github.com/root-project/root/blob/master/documentation/doxygen/converttonotebook.py\">ROOTBOOK-izer</a> from the macro found in the ROOT repository  on Tuesday, May 19, 2026 at 08:33 PM.</small></i>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "b12e6b4d",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:33:05.308935Z",
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     "shell.execute_reply": "2026-05-19T20:33:05.323200Z"
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   "outputs": [],
   "source": [
    "%%cpp -d\n",
    "#include \"RooRealVar.h\"\n",
    "#include \"RooDataSet.h\"\n",
    "#include \"RooGaussian.h\"\n",
    "#include \"RooPolynomial.h\"\n",
    "#include \"RooAddPdf.h\"\n",
    "#include \"RooProdPdf.h\"\n",
    "#include \"RooFitResult.h\"\n",
    "#include \"RooPlot.h\"\n",
    "#include \"TCanvas.h\"\n",
    "#include \"TAxis.h\"\n",
    "#include \"TH1.h\"\n",
    "using namespace RooFit;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fb6b171f",
   "metadata": {},
   "source": [
    "Create model and dataset\n",
    "----------------------------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d83ad2d7",
   "metadata": {},
   "source": [
    "Construct a Gaussian pdf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "16ff8cf5",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:33:05.325588Z",
     "iopub.status.busy": "2026-05-19T20:33:05.325471Z",
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     "shell.execute_reply": "2026-05-19T20:33:05.690321Z"
    }
   },
   "outputs": [],
   "source": [
    "RooRealVar x(\"x\", \"x\", -10, 10);\n",
    "\n",
    "RooRealVar m(\"m\", \"m\", 0, -10, 10);\n",
    "RooRealVar s(\"s\", \"s\", 2, 0.1, 10);\n",
    "RooGaussian gauss(\"gauss\", \"gauss(x,m,s)\", x, m, s);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7c856e3e",
   "metadata": {},
   "source": [
    "Construct a flat pdf (polynomial of 0th order)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "42529dcf",
   "metadata": {
    "collapsed": false,
    "execution": {
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     "shell.execute_reply": "2026-05-19T20:33:05.904128Z"
    }
   },
   "outputs": [],
   "source": [
    "RooPolynomial poly(\"poly\", \"poly(x)\", x);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "34038356",
   "metadata": {},
   "source": [
    "Construct model = f*gauss + (1-f)*poly"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "ee1b8014",
   "metadata": {
    "collapsed": false,
    "execution": {
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     "shell.execute_reply": "2026-05-19T20:33:06.114548Z"
    }
   },
   "outputs": [],
   "source": [
    "RooRealVar f(\"f\", \"f\", 0.5, 0., 1.);\n",
    "RooAddPdf model(\"model\", \"model\", RooArgSet(gauss, poly), f);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8fc592b6",
   "metadata": {},
   "source": [
    "Generate small dataset for use in fitting below"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "fc448fee",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:33:06.117283Z",
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     "shell.execute_reply": "2026-05-19T20:33:06.325091Z"
    }
   },
   "outputs": [],
   "source": [
    "std::unique_ptr<RooDataSet> d{model.generate(x, 50)};"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8024ba5c",
   "metadata": {},
   "source": [
    "Create constraint pdf\n",
    "-----------------------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cbabf47f",
   "metadata": {},
   "source": [
    "Construct Gaussian constraint pdf on parameter f at 0.8 with resolution of 0.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "30379827",
   "metadata": {
    "collapsed": false,
    "execution": {
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     "shell.execute_reply": "2026-05-19T20:33:06.535641Z"
    }
   },
   "outputs": [],
   "source": [
    "RooGaussian fconstraint(\"fconstraint\", \"fconstraint\", f, 0.8, 0.2);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "74b63105",
   "metadata": {},
   "source": [
    "METHOD 1 - Add internal constraint to model\n",
    "-------------------------------------------------------------------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cb9fb5fb",
   "metadata": {},
   "source": [
    "Multiply constraint term with regular pdf using RooProdPdf\n",
    "Specify in fitTo() that internal constraints on parameter f should be used"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "60d4d351",
   "metadata": {},
   "source": [
    "Multiply constraint with pdf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "59300fcb",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:33:06.538323Z",
     "iopub.status.busy": "2026-05-19T20:33:06.538201Z",
     "iopub.status.idle": "2026-05-19T20:33:06.746919Z",
     "shell.execute_reply": "2026-05-19T20:33:06.746160Z"
    }
   },
   "outputs": [],
   "source": [
    "RooProdPdf modelc(\"modelc\", \"model with constraint\", RooArgSet(model, fconstraint));"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "adef0070",
   "metadata": {},
   "source": [
    "Fit model (without use of constraint term)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "0a91f2b4",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:33:06.748931Z",
     "iopub.status.busy": "2026-05-19T20:33:06.748803Z",
     "iopub.status.idle": "2026-05-19T20:33:06.958704Z",
     "shell.execute_reply": "2026-05-19T20:33:06.958086Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[#1] INFO:Fitting -- RooAbsPdf::fitTo(model) fixing normalization set for coefficient determination to observables in data\n",
      "[#1] INFO:Fitting -- using generic CPU library compiled with no vectorizations\n",
      "[#1] INFO:Fitting -- Creation of NLL object took 798.163 μs\n",
      "[#1] INFO:Fitting -- RooAddition::defaultErrorLevel(nll_model_modelData) Summation contains a RooNLLVar, using its error level\n",
      "[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only\n"
     ]
    }
   ],
   "source": [
    "std::unique_ptr<RooFitResult> r1{model.fitTo(*d, Save(), PrintLevel(-1))};"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ad0e12e8",
   "metadata": {},
   "source": [
    "Fit modelc with constraint term on parameter f"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "1c484447",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:33:06.960056Z",
     "iopub.status.busy": "2026-05-19T20:33:06.959940Z",
     "iopub.status.idle": "2026-05-19T20:33:07.169987Z",
     "shell.execute_reply": "2026-05-19T20:33:07.169347Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[#1] INFO:Minimization --  Including the following constraint terms in minimization: (fconstraint)\n",
      "[#1] INFO:Minimization -- The global observables are not defined , normalize constraints with respect to the parameters (f)\n",
      "[#1] INFO:Fitting -- RooAbsPdf::fitTo(modelc) fixing normalization set for coefficient determination to observables in data\n",
      "[#1] INFO:Fitting -- Creation of NLL object took 1.97668 ms\n",
      "[#1] INFO:Fitting -- RooAddition::defaultErrorLevel(nll_modelc_modelData) Summation contains a RooNLLVar, using its error level\n",
      "[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only\n"
     ]
    }
   ],
   "source": [
    "std::unique_ptr<RooFitResult> r2{modelc.fitTo(*d, Constrain(f), Save(), PrintLevel(-1))};"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "57fa5481",
   "metadata": {},
   "source": [
    "METHOD 2 -  Specify external constraint when fitting\n",
    "-------------------------------------------------------------------------------------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f47fb054",
   "metadata": {},
   "source": [
    "Construct another Gaussian constraint pdf on parameter f at 0.2 with resolution of 0.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "432ffb31",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:33:07.171399Z",
     "iopub.status.busy": "2026-05-19T20:33:07.171283Z",
     "iopub.status.idle": "2026-05-19T20:33:07.379675Z",
     "shell.execute_reply": "2026-05-19T20:33:07.379200Z"
    }
   },
   "outputs": [],
   "source": [
    "RooGaussian fconstext(\"fconstext\", \"fconstext\", f, 0.2, 0.1);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a4c6c184",
   "metadata": {},
   "source": [
    "Fit with external constraint"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "5173aff2",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:33:07.381487Z",
     "iopub.status.busy": "2026-05-19T20:33:07.381376Z",
     "iopub.status.idle": "2026-05-19T20:33:07.591272Z",
     "shell.execute_reply": "2026-05-19T20:33:07.590757Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[#1] INFO:Minimization --  Including the following constraint terms in minimization: (fconstext)\n",
      "[#1] INFO:Minimization -- The global observables are not defined , normalize constraints with respect to the parameters (f,m,s)\n",
      "[#1] INFO:Fitting -- RooAbsPdf::fitTo(model) fixing normalization set for coefficient determination to observables in data\n",
      "[#1] INFO:Fitting -- Creation of NLL object took 251.01 μs\n",
      "[#1] INFO:Fitting -- RooAddition::defaultErrorLevel(nll_model_modelData) Summation contains a RooNLLVar, using its error level\n",
      "[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only\n"
     ]
    }
   ],
   "source": [
    "std::unique_ptr<RooFitResult> r3{model.fitTo(*d, ExternalConstraints(fconstext), Save(), PrintLevel(-1))};"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2b46ee50",
   "metadata": {},
   "source": [
    "Print the fit results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "79670514",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:33:07.593116Z",
     "iopub.status.busy": "2026-05-19T20:33:07.592952Z",
     "iopub.status.idle": "2026-05-19T20:33:07.801394Z",
     "shell.execute_reply": "2026-05-19T20:33:07.800954Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "fit result without constraint (data generated at f=0.5)\n",
      "\n",
      "  RooFitResult: minimized FCN value: 134.849, estimated distance to minimum: 2.11658e-05\n",
      "                covariance matrix quality: Full, accurate covariance matrix\n",
      "                Status : MINIMIZE=0 HESSE=0 \n",
      "\n",
      "    Floating Parameter  InitialValue    FinalValue +/-  Error     GblCorr.\n",
      "  --------------------  ------------  --------------------------  --------\n",
      "                     f    5.0000e-01    6.4987e-01 +/-  1.21e-01  <none>\n",
      "                     m    0.0000e+00    7.1824e-01 +/-  4.97e-01  <none>\n",
      "                     s    2.0000e+00    2.1880e+00 +/-  4.61e-01  <none>\n",
      "\n",
      "fit result with internal constraint (data generated at f=0.5, constraint is f=0.8+/-0.2)\n",
      "\n",
      "  RooFitResult: minimized FCN value: 134.191, estimated distance to minimum: 0.000427811\n",
      "                covariance matrix quality: Full, accurate covariance matrix\n",
      "                Status : MINIMIZE=0 HESSE=0 \n",
      "\n",
      "    Floating Parameter  InitialValue    FinalValue +/-  Error     GblCorr.\n",
      "  --------------------  ------------  --------------------------  --------\n",
      "                     f    6.4987e-01    6.8952e-01 +/-  1.01e-01  <none>\n",
      "                     m    7.1824e-01    7.0939e-01 +/-  4.97e-01  <none>\n",
      "                     s    2.1880e+00    2.2657e+00 +/-  4.74e-01  <none>\n",
      "\n",
      "fit result with (another) external constraint (data generated at f=0.5, constraint is f=0.2+/-0.1)\n",
      "\n",
      "  RooFitResult: minimized FCN value: 137.195, estimated distance to minimum: 0.000256905\n",
      "                covariance matrix quality: Full, accurate covariance matrix\n",
      "                Status : MINIMIZE=0 HESSE=0 \n",
      "\n",
      "    Floating Parameter  InitialValue    FinalValue +/-  Error     GblCorr.\n",
      "  --------------------  ------------  --------------------------  --------\n",
      "                     f    6.8952e-01    3.6252e-01 +/-  8.15e-02  <none>\n",
      "                     m    7.0939e-01    7.1394e-01 +/-  5.87e-01  <none>\n",
      "                     s    2.2657e+00    1.7027e+00 +/-  4.74e-01  <none>\n",
      "\n"
     ]
    }
   ],
   "source": [
    "cout << \"fit result without constraint (data generated at f=0.5)\" << endl;\n",
    "r1->Print(\"v\");\n",
    "cout << \"fit result with internal constraint (data generated at f=0.5, constraint is f=0.8+/-0.2)\" << endl;\n",
    "r2->Print(\"v\");\n",
    "cout << \"fit result with (another) external constraint (data generated at f=0.5, constraint is f=0.2+/-0.1)\" << endl;\n",
    "r3->Print(\"v\");"
   ]
  }
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